Parkinson's men go into Sunday's second round tie with the Vanarama Conference side off the back of a current four-match unbeaten run - a sequence that begin with victory in the F.A Cup over FC Halifax Town in the previous round.
A lot of the talk going into Sunday's tie with non-league Darts will inevitably centre around possible giant-killings, battling against the underdog and third round draws, but Parkinson wants to try and put that all to one side if he can.
The City chief would instead simply prefer his players to focus purely on keeping their performance levels up to where they have been over the past few weeks.
Parkinson said: "Regardless of whether this Sunday's game was a cup tie or a league match, we want to keep our (unbeaten) run going.
"We want to keep playing well as a team. Individuals within our team are playing with confidence at the moment. We want that to remain the case while pushing on for more.
"There is no better feeling in football than when you win.
"We are on a decent run at present but we have to keep it going.
"We know that there is the prize of getting into the third round draw if we win but it is a big game for us regardless because we want to keep this run going.
"We are determined to put on a good show and to play as well as we can to give ourselves the best possible chance of progressing."
Following City's hard-fought victory over Halifax in the first round, this Sunday's encounter with Dartford will, of course, be the Bantams' second successive F.A Cup tie against non-league opponents.
With Dartford heading to the Coral Windows Stadium this weekend undoubtedly dreaming that they can cause an upset, Parkinson believes City will benefit from knowing already what it is like coming up against a side hungry for a cup shock.
Parkinson added: "Going into this match against a non-league side, we have the experience of having played Halifax already this season.
"We have to use that sort of experience for this game on Sunday because we remember how tough that game was and how physical it was.
"We remember how hard we had to work for the result, and this will be no different come Sunday."
As mentioned earlier this week on the official website, Parkinson has left no stone unturned in his pursuit for information on Dartford following last month's draw.
Parkinson has had Dartford watched in each of their last four games, with the Bantams chief himself travelling down south twice to watch them live in person.
Parkinson continued: "When you draw a team outside your division, you sometimes don't quite know the players as well as you might do if they were playing in your own league.
"With that in mind, we wanted to give ourselves the best chance possible to know everything we could about Dartford going into this game.
"We wanted to build up our knowledge on them basically - we'd be crazy if we didn't do that.
"In both of the games I've seen them play, they have performed well and they perhaps didn't deserve to lose as they did.
"They have some decent footballers and they will look to come here at the weekend and play football. They also have the threat from long throws and set-pieces.
"Equally though, if we can stand up to that, I feel they are a team we can create chances against.
"In similar fashion to how we spoke about Halifax before that match, we know we will have to be strong and resilient on Sunday but also calm and patient when we have the ball."